List questions from rearrangement-inequality

232

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How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

Published on 19 Mar 2026 - 19:54

919

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How is symmetry in an inequality determined?

Published on 22 Mar 2026 - 23:23

173

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Does $(\sum_{i=1}^n a_i^{1.5})^2 - \sum_{i=1}^n a_i \; \sum_{i=1}^n a_i a_{i+1} > 0$ hold for $n \leq 8$?

Published on 24 Mar 2026 - 13:11

82

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Generalization of the Pólya–Szegő inequality

Published on 22 Mar 2026 - 22:13

150

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Is it true that $\frac {a}{a+b}+\frac {b}{b+c}+\frac {c}{c+a}\geq \frac32$ if $a+b+c=1$?

Published on 23 Mar 2026 - 8:48

172

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How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Published on 23 Mar 2026 - 11:27

65

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Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Published on 22 Mar 2026 - 16:54

73

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Show that problem and that equality if fulfilled iff a=b

Published on 23 Mar 2026 - 2:57

185

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replacing Inequalities

Published on 16 Mar 2026 - 20:25

394

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Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

Published on 22 Mar 2026 - 21:23

146

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Show that $a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}$ holds for $a,b,c>0$

Published on 23 Mar 2026 - 1:04

444

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Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Published on 25 Mar 2026 - 4:43

100

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Application of Chebyschev inequality

Published on 25 Mar 2026 - 3:07

75

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Optimization of sum of squares over permutations

Published on 25 Mar 2026 - 4:39

83

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How does the number $3$ help in this (probably Cauchy-based) inequality?

Published on 25 Mar 2026 - 4:54

List Question

How to prove this interesting inequality: $\frac{5x+3y+z}{5z+3y+x}+\frac{5y+3z+x}{5x+3z+y}+\frac{5z+3x+y}{5y+3x+z}\ge 3$?

How is symmetry in an inequality determined?

Does $(\sum_{i=1}^n a_i^{1.5})^2 - \sum_{i=1}^n a_i \; \sum_{i=1}^n a_i a_{i+1} > 0$ hold for $n \leq 8$?

Generalization of the Pólya–Szegő inequality

Is it true that $\frac {a}{a+b}+\frac {b}{b+c}+\frac {c}{c+a}\geq \frac32$ if $a+b+c=1$?

How do I prove this inequality: $a^2+b^2+c^2 \geq ab+bc+ac$?

Prove that $\sum_{cyc} {\frac{y-x}{y^2-1}}$ >0

Show that problem and that equality if fulfilled iff a=b

replacing Inequalities

Rearrangement inequality and minimal value of $\frac{\sin^3x}{\cos x} +\frac{\cos^3x}{\sin x}$

Show that $a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}$ holds for $a,b,c>0$

Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Application of Chebyschev inequality

Optimization of sum of squares over permutations

How does the number $3$ help in this (probably Cauchy-based) inequality?

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